Initial Acceleration of Wood in Water

[sona1177]

Homework Statement

For the following problem:

A piece of balsa wood with density .50 g/cm^3 is released under water. What is its initial acceleration?

I have gotten this far:

Fnet=Fbuoy-mg
-ma=p(water)gV(displaced)- p(wood)g(Vdisplaced)
=(p(water)-p(wood))gV=-ma

where p="rho"

But in this equation I have three unknowns: mass of wood, Volume displaced, and the acceleration

How do I get around this? I've tried using equations involving Specific Gravity but that doesn't help, it leads be down an unproductive road of manipulating equations that don't have solutions because there are too many unknowns.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

You replaced the mass on the right hand side with its equivalent in terms of density and volume. Do the same with the mass on the left hand side.

 

[sona1177]

Thank you! At first I had a negative sign in front of the m, which gave a negative acceleration of -9.8 m/s^2. But the answer is +9.8 m/s^2. Is this because the balsa wood is less dense than the water, so it can only rise, thereby giving + acceleration?

 

[Doc Al]

Thank you! At first I had a negative sign in front of the m, which gave a negative acceleration of -9.8 m/s^2. But the answer is +9.8 m/s^2. Is this because the balsa wood is less dense than the water, so it can only rise, thereby giving + acceleration?

That's right. The net force is upward, thus the acceleration is upward. (You shouldn't have put a negative sign in front of the ma. Newton's law says ΣF = ma, not ΣF = -ma.)

 

[sona1177]

That's right. (You shouldn't have put a negative sign in front of the ma. Newton's law says ΣF = ma, not ΣF = -ma.)

But when I know the acceleration is negative, I usually just put the negative sign in there. Then all I have to do is work in terms of magnitudes.

For example if a block of metal was released in the water with a density larger than water, then I'd place the negative sign in front of acceleration and set the equation as

-ma=Fbuoy-mg

This way I can work in terms of magnitudes since signs are taken care of.

It's alright to put the negative sign if I know the object will sink right?

 

[Doc Al]

Personally, I would not do that. Use a consistent sign convention (up = +) and let the equation do the work.

(It's ok to take shortcuts--as long as you know what you're doing. But you certainly don't want to show such an equation in work that's being marked.)

 

[sona1177]

Personally, I would not do that. Use a consistent sign convention (up = +) and let the equation do the work.

(It's ok to take shortcuts--as long as you know what you're doing. But you certainly don't want to show such an equation in work that's being marked.)

Thank you for the advice! :)